I'm not the best with forms, but my guess is you built a query and used that as the form's datasource. This is incorrect. Every form that will allow data manipulation (add/edit/delete) should be based on just one table. Sometimes, like this case, it will mean employing a sub-form.
You have 4 tables, that means 4 forms. Institutions, All Applicants (you should really remove the space from all table and field names), Awarded Grants and Fiscal Funding will have their own form. Fiscal Funding will be the unique one, it will have its own form, but that form will be a subform on the Awarded Grants form. That way you can add multiple years of funding to a grant.
You might be better off heading to the Forms section now and asking specific questions there.